US10728081B1ActiveUtility

Wideband TX IQ imbalance estimation

87
Assignee: TOSHIBA KKPriority: Mar 15, 2019Filed: Mar 15, 2019Granted: Jul 28, 2020
Est. expiryMar 15, 2039(~12.7 yrs left)· nominal 20-yr term from priority
H04L 27/364H04L 27/0014H04L 27/2657H04L 2027/004H04L 27/3863H04L 2027/0042
87
PatentIndex Score
10
Cited by
12
References
17
Claims

Abstract

A computer-implemented method of estimating IQ imbalance in a communication system including a transmitter and a receiver. The method includes: defining a system model in which a transmitted signal is affected by TX IQ imbalance, carrier frequency offset (CFO) and RX IQ imbalance; controlling a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and estimating unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance.

Claims

exact text as granted — not AI-modified
The invention claimed is: 
     
       1. A method of estimating in-phase and quadrature (IQ) imbalance, the method at least partially performed by electronic circuitry and comprising:
 defining a system model in which a transmitted signal is affected by transmitter IQ (TX IQ) imbalance, carrier frequency offset (CFO) and receiver IQ (RX IQ) imbalance; 
 controlling a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimating unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance, 
 wherein the CFO is chosen to provide a relative frequency offset of at least 0.001, at least 0.005 or at least 0.05. 
 
     
     
       2. A method of estimating in-phase and quadrature (IQ) imbalance, the method at least partially performed by electronic circuitry and comprising:
 defining a system model in which a transmitted signal is affected by transmitter IQ (TX IQ) imbalance, carrier frequency offset (CFO) and receiver IQ (RX IQ) imbalance; 
 controlling a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimating unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance, 
 wherein the TX IQ imbalance is defined as 
 
       
         
           
             
               
                 
                   y 
                   
                     k 
                     , 
                     l 
                   
                 
                 ⁡ 
                 
                   ( 
                   i 
                   ) 
                 
               
               = 
               
                 
                   
                     
                       α 
                       k 
                       
                         ( 
                         T 
                         ) 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       x 
                       
                         k 
                         , 
                         l 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
                 + 
                 
                   
                     
                       β 
                       
                         - 
                         k 
                       
                       
                         
                           ( 
                           T 
                           ) 
                         
                         * 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       x 
                       
                         
                           - 
                           k 
                         
                         , 
                         l 
                       
                       * 
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
               
             
           
         
         where k indicates a subcarrier, l indicates a time index, i=1, . . . , N tx  is a transmit channel index and α k   (T) , β k   (T)  are IQ imbalance coefficients at the transmitter. 
       
     
     
       3. A method of estimating in-phase and quadrature (IQ) imbalance, the method at least partially performed by electronic circuitry and comprising:
 defining a system model in which a transmitted signal is affected by transmitter IQ (TX IQ) imbalance, carrier frequency offset (CFO) and receiver IQ (RX IQ) imbalance; 
 controlling a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimating unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance, 
 wherein the system model further comprises an inter-channel interference defined as 
 
       
         
           
             
               
                 
                   z 
                   
                     k 
                     , 
                     l 
                   
                 
                 ⁡ 
                 
                   ( 
                   m 
                   ) 
                 
               
               = 
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   
                     N 
                     tx 
                   
                 
                 ⁢ 
                 
                   
                     
                       h 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       
                         m 
                         , 
                         i 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       y 
                       
                         k 
                         , 
                         l 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
               
             
           
         
         where m=1, . . . , N rx  is a receive channel index and h is a channel coefficient. 
       
     
     
       4. A method of estimating in-phase and quadrature (IQ) imbalance, the method at least partially performed by electronic circuitry and comprising:
 defining a system model in which a transmitted signal is affected by transmitter IQ (TX IQ) imbalance, carrier frequency offset (CFO) and receiver IQ (RX IQ) imbalance; 
 controlling a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimating unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance, 
 wherein the CFO is defined as
     w   k,l ( m )= e   jϕl   z   k,l ( m ) 
 
 where ϕ represents a phase shift caused by the CFO. 
 
     
     
       5. The method of  claim 4  wherein the RX IQ imbalance is defined as 
       
         
           
             
               
                 
                   r 
                   
                     k 
                     , 
                     l 
                   
                 
                 ⁡ 
                 
                   ( 
                   m 
                   ) 
                 
               
               = 
               
                 
                   
                     
                       α 
                       k 
                       
                         ( 
                         R 
                         ) 
                       
                     
                     ⁡ 
                     
                       ( 
                       m 
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       w 
                       
                         k 
                         , 
                         l 
                       
                     
                     ⁡ 
                     
                       ( 
                       m 
                       ) 
                     
                   
                 
                 + 
                 
                   
                     
                       β 
                       
                         - 
                         k 
                       
                       
                         
                           ( 
                           R 
                           ) 
                         
                         * 
                       
                     
                     ⁡ 
                     
                       ( 
                       m 
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       w 
                       
                         
                           - 
                           k 
                         
                         , 
                         l 
                       
                       * 
                     
                     ⁡ 
                     
                       ( 
                       m 
                       ) 
                     
                   
                 
               
             
           
         
         where α k   (R) , β k   (R)  are IQ imbalance coefficients at the receiver. 
       
     
     
       6. The method of  claim 5  wherein the system model is defined as 
       
         
           
             
               
                 r 
                 
                   k 
                   , 
                   l 
                 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ϕ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             l 
                           
                         
                         ⁢ 
                         
                           A 
                           k 
                         
                       
                       + 
                       
                         
                           e 
                           
                             
                               - 
                               j 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ϕ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             l 
                           
                         
                         ⁢ 
                         
                           B 
                           k 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     x 
                     
                       k 
                       , 
                       l 
                     
                   
                 
                 + 
                 
                   
                     ( 
                     
                       
                         
                           e 
                           
                             j 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ϕ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             l 
                           
                         
                         ⁢ 
                         
                           C 
                           k 
                         
                       
                       + 
                       
                         
                           e 
                           
                             
                               - 
                               j 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ϕ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             l 
                           
                         
                         ⁢ 
                         
                           D 
                           k 
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     x 
                     
                       
                         - 
                         k 
                       
                       , 
                       l 
                     
                     * 
                   
                 
               
             
           
         
         where r k,l  is a N rx ×1 vector, A k ,B k ,C k ,D k  are N rx ×N tx  matrices and y k,l  is a N tx ×1 vector. 
       
     
     
       7. The method of  claim 6  wherein the matrices are defined as: 
       
         
           
             
               
                 
                   A 
                   k 
                 
                 ⁡ 
                 
                   ( 
                   
                     m 
                     , 
                     i 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     h 
                     k 
                   
                   ⁡ 
                   
                     ( 
                     
                       m 
                       , 
                       i 
                     
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     α 
                     k 
                     
                       ( 
                       T 
                       ) 
                     
                   
                   ⁡ 
                   
                     ( 
                     i 
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     α 
                     k 
                     
                       ( 
                       R 
                       ) 
                     
                   
                   ⁡ 
                   
                     ( 
                     m 
                     ) 
                   
                 
               
             
           
         
         
           
             
               
                 
                   B 
                   k 
                 
                 ⁡ 
                 
                   ( 
                   
                     m 
                     , 
                     i 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     h 
                     
                       - 
                       k 
                     
                     * 
                   
                   ⁡ 
                   
                     ( 
                     
                       m 
                       , 
                       i 
                     
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     β 
                     k 
                     
                       ( 
                       T 
                       ) 
                     
                   
                   ⁡ 
                   
                     ( 
                     i 
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     β 
                     
                       - 
                       k 
                     
                     
                       
                         ( 
                         R 
                         ) 
                       
                       * 
                     
                   
                   ⁡ 
                   
                     ( 
                     m 
                     ) 
                   
                 
               
             
           
         
         
           
             
               
                 
                   C 
                   k 
                 
                 ⁡ 
                 
                   ( 
                   
                     m 
                     , 
                     i 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     h 
                     k 
                   
                   ⁡ 
                   
                     ( 
                     
                       m 
                       , 
                       i 
                     
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     β 
                     
                       - 
                       k 
                     
                     
                       
                         ( 
                         T 
                         ) 
                       
                       * 
                     
                   
                   ⁡ 
                   
                     ( 
                     i 
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     α 
                     k 
                     
                       ( 
                       R 
                       ) 
                     
                   
                   ⁡ 
                   
                     ( 
                     m 
                     ) 
                   
                 
               
             
           
         
         
           
             
               
                 
                   D 
                   k 
                 
                 ⁡ 
                 
                   ( 
                   
                     m 
                     , 
                     i 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     h 
                     
                       - 
                       k 
                     
                     * 
                   
                   ⁡ 
                   
                     ( 
                     
                       m 
                       , 
                       i 
                     
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     α 
                     
                       - 
                       k 
                     
                     
                       
                         ( 
                         T 
                         ) 
                       
                       
                         
                             
                         
                         * 
                       
                     
                   
                   ⁡ 
                   
                     ( 
                     i 
                     ) 
                   
                 
                 ⁢ 
                 
                   
                     
                       β 
                       
                         - 
                         k 
                       
                       
                         
                           ( 
                           R 
                           ) 
                         
                         * 
                       
                     
                     ⁡ 
                     
                       ( 
                       m 
                       ) 
                     
                   
                   . 
                 
               
             
           
         
       
     
     
       8. The method of  claim 7  wherein the TX IQ imbalance is obtained from 
       
         
           
             
               
                 
                   
                     
                       C 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       
                         m 
                         , 
                         i 
                       
                       ) 
                     
                   
                   
                     
                       A 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       
                         m 
                         , 
                         i 
                       
                       ) 
                     
                   
                 
                 = 
                 
                   
                     
                       β 
                       
                         - 
                         k 
                       
                       
                         
                           ( 
                           T 
                           ) 
                         
                         * 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   
                     
                       α 
                       k 
                       
                         ( 
                         T 
                         ) 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
               
               . 
             
           
         
       
     
     
       9. The method of  claim 7  wherein the RX IQ imbalance is obtained from 
       
         
           
             
               
                 
                   
                     
                       D 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       
                         m 
                         , 
                         i 
                       
                       ) 
                     
                   
                   
                     
                       A 
                       
                         - 
                         k 
                       
                       * 
                     
                     ⁡ 
                     
                       ( 
                       
                         m 
                         , 
                         i 
                       
                       ) 
                     
                   
                 
                 = 
                 
                   
                     
                       β 
                       
                         - 
                         k 
                       
                       
                         
                           ( 
                           R 
                           ) 
                         
                         * 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   
                     
                       α 
                       
                         - 
                         k 
                       
                       
                         
                           ( 
                           R 
                           ) 
                         
                         * 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
               
               . 
             
           
         
       
     
     
       10. The method of  claim 7  wherein the step of estimating the unknown parameters comprises estimating the matrices A k , B k ,C k ,D k  using the pre-defined training sequence wherein 
       
         
           
             
               
                 ( 
                 
                   
                     r 
                     
                       k 
                       , 
                       0 
                     
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   … 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     r 
                     
                       k 
                       , 
                       
                         L 
                         - 
                         1 
                       
                     
                   
                 
                 ) 
               
               = 
               
                 
                   
                     ( 
                     
                       
                         A 
                         k 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         B 
                         k 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         C 
                         k 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         D 
                         k 
                       
                     
                     ) 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 k 
                                 , 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 k 
                                 , 
                                 1 
                               
                             
                           
                         
                         
                           … 
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     L 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 k 
                                 , 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   
                                       
                                   
                                   ⁢ 
                                   ϕ 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 k 
                                 , 
                                 0 
                               
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 k 
                                 , 
                                 1 
                               
                             
                           
                         
                         
                           … 
                         
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     L 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 k 
                                 , 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   - 
                                   k 
                                 
                                 , 
                                 0 
                               
                               * 
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   - 
                                   k 
                                 
                                 , 
                                 1 
                               
                               * 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             
                               e 
                               
                                 j 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     L 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   - 
                                   k 
                                 
                                 , 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                               * 
                             
                           
                         
                       
                       
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 0 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   - 
                                   k 
                                 
                                 , 
                                 0 
                               
                               * 
                             
                           
                         
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   - 
                                   k 
                                 
                                 , 
                                 1 
                               
                               * 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             
                               e 
                               
                                 
                                   - 
                                   j 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ϕ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   
                                     L 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               x 
                               
                                 
                                   - 
                                   k 
                                 
                                 , 
                                 
                                   L 
                                   - 
                                   1 
                                 
                               
                               * 
                             
                           
                         
                       
                     
                     ) 
                   
                   ⁢ 
                   R 
                 
                 = 
                 EM 
               
             
           
         
         where R is a N rx ×L matrix, E is a N rx ×4N tx  matrix and M is a 4N tx ×L matrix. 
       
     
     
       11. The method of  claim 10  comprising estimating the matrices A k ,B k ,C k ,D k  using a least-squares estimation method in accordance with
     Ê=RM   H ( MM   H ) −1    
 where H indicates a complex conjugate transpose. 
 
     
     
       12. A method of compensating for in-phase quadrature (IQ) imbalance in a communication system comprising a transmitter and a receiver, the method comprising:
 estimating the IQ imbalance in accordance with  claim 1 ; 
 instructing the transmitter to use the estimated transmitter IQ (TX IQ) imbalance to pre-distort a transmitted signal to remove the effect of the TX IQ imbalance; and 
 instructing the receiver to use the estimated receiver IQ (RX IQ) imbalance to compensate a received signal to remove the effect of the RX IQ imbalance. 
 
     
     
       13. An electronic apparatus comprising a processor and a memory, the processor coupled to the memory and configured to:
 define a system model in which a transmitted signal is affected by transmitter in-phase and quadrature (TX IQ) imbalance, carrier frequency offset (CFO) and receiver in-phase and quadrature (RX IQ) imbalance; 
 control a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimate unknown parameters in the system model using a pre-defined training sequence to determine the TX TO imbalance and the RX IQ imbalance, 
 wherein the CFO is chosen to provide a relative frequency offset of at least 0.001, at least 0.005 or at least 0.05. 
 
     
     
       14. The electronic apparatus of  claim 13  configured as a mobile phone base-station, a digital video broadcasting (DVB) transmitter, a wideband wireless transmitter or a millimetre wave point-to-point transmitter. 
     
     
       15. An electronic apparatus comprising a processor and a memory, the processor coupled to the memory and configured to:
 define a system model in which a transmitted signal is affected by transmitter in-phase and quadrature (TX IQ) imbalance, carrier frequency offset (CFO) and receiver in-phase and quadrature (RX IQ) imbalance; 
 control a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimate unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance, 
 wherein the TX IQ imbalance is defined as 
 
       
         
           
             
               
                 
                   y 
                   
                     k 
                     , 
                     l 
                   
                 
                 ⁡ 
                 
                   ( 
                   i 
                   ) 
                 
               
               = 
               
                 
                   
                     
                       α 
                       k 
                       
                         ( 
                         T 
                         ) 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       x 
                       
                         k 
                         , 
                         l 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
                 + 
                 
                   
                     
                       β 
                       
                         - 
                         k 
                       
                       
                         
                           ( 
                           T 
                           ) 
                         
                         * 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       x 
                       
                         
                           - 
                           k 
                         
                         , 
                         l 
                       
                       * 
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
               
             
           
         
         where k indicates a subcarrier, l indicates a time index, i=1, . . . , N tx  is a transmit channel index and α k   (T) , β k   (T)  are IQ imbalance coefficients at the transmitter. 
       
     
     
       16. An electronic apparatus comprising a processor and a memory, the processor coupled to the memory and configured to:
 define a system model in which a transmitted signal is affected by transmitter in-phase and quadrature (TX IQ) imbalance, carrier frequency offset (CFO) and receiver in-phase and quadrature (RX IQ) imbalance; 
 control a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimate unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance, 
 wherein the system model further comprises an inter-channel interference defined as 
 
       
         
           
             
               
                 
                   z 
                   
                     k 
                     , 
                     l 
                   
                 
                 ⁡ 
                 
                   ( 
                   m 
                   ) 
                 
               
               = 
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   
                     N 
                     tx 
                   
                 
                 ⁢ 
                 
                   
                     
                       h 
                       k 
                     
                     ⁡ 
                     
                       ( 
                       
                         m 
                         , 
                         i 
                       
                       ) 
                     
                   
                   ⁢ 
                   
                     
                       y 
                       
                         k 
                         , 
                         l 
                       
                     
                     ⁡ 
                     
                       ( 
                       i 
                       ) 
                     
                   
                 
               
             
           
         
         where m=1, . . . , N rx  is a receive channel index and h is a channel coefficient. 
       
     
     
       17. An electronic apparatus comprising a processor and a memory, the processor coupled to the memory and configured to:
 define a system model in which a transmitted signal is affected by transmitter in-phase and quadrature (TX IQ) imbalance, carrier frequency offset (CFO) and receiver in-phase and quadrature (RX IQ) imbalance; 
 control a local oscillator at the transmitter to introduce a known carrier frequency offset (CFO) during a calibration; and 
 estimate unknown parameters in the system model using a pre-defined training sequence to determine the TX IQ imbalance and the RX IQ imbalance, 
 wherein the CFO is defined as
     w   k,l ( m )= e   jϕl   z   k,l ( m ) 
 
 where ϕ represents a phase shift caused by the CFO.

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